Well if you have a large image ( pixel size ) for desktop, using one half that size ( in pixels ) could give you 1/4 of the MB payload. A cropped image may be far better for that format and the filesizes much smaller.
Within Xara you have an 960px desktop version, with an image 960px wide. You name it 'Desktop'. You create a 480px mobile variant. The 960px version image is too large so you resize it to 480px. Xara creates two images:

Desktop.jpg size =163.45 kB which is served to the desktop PC

Desktop1.jpg size =30.35 kB which is served to the desktop PC

If you crop the Main version image and place it on the mobile variant and resize that to 480px and name it 'Cropped'. Xara creates the image:

Cropped.jpg size =25.84 kB (dependant on the reduced colours)

So there's no great saving between the resized and cropped images. Aesthetically a cropped image MAY look better but the filesize saving is small.